Quantitative analysis of in vitro systems of B cell activation and plasma cell differentiation can be used to estimate parameters of B cell behavior necessary for immune responses, and to suggest strategies for manipulation of B cell immune responses. Antibody mediated rejection of kidney transplants involves activation of B cells, which produce plasma cells that secrete antibodies against cell surface markers present in the transplant. While a variety of therapeutic agents can affect B cell proliferation, death, and differentiation, we currently lack robust quantitative models to guide the design of clinical trials. The overall goal of this work is to develop such a framework. Our first aim is to develop and experimentally validate a multi-type Bellman- Harris branching process of B cell proliferation and terminal plasma cell differentiation. Current models of B cell differentiation are either continuous population based ordinary differential equation (ODE) models or non-quantitative graphical representations of experimental observations. We propose an alternative approach, a multi-type branching stochastic process coupled with discrete event, agent based modeling of individual virtual B cells in silico. Model parameters will be estimated and the model validated with new statistical methods described in Aim 2 using data from a novel in vitro plasma cell differentiation system we have developed. Our second aim is to develop and experimentally validate rigorous statistical methods for lymphocyte kinetic parameter estimation from CFSE labeling experiments. We will develop novel statistical methods (estimation, test, goodness-of-fit) for the quantitative analysis of CFSE data. In contrast to currently available approaches, the proposed methods will make it feasible to estimate parameters of cell activation, proliferation, differentiation and death. We will study their theoretical properties (such as consistency and asymptotic normality of estimators), provide expressions for the variance-covariance matrix of the proposed estimators, and evaluate their finite sample performance in extensive simulation studies. Our third aim is o model the effects of agents that impede the GO->G1 progression (sirolimus), delay S/M transition (mycophenolate mofetil), or prevent cell cycle exit (IL-6 antagonists) on plasma cell generation and perform in vitro model validation. We will use a novel in vitro culture system to drive human B cells from activation to terminal plasma cell differentiation. Using the techniques developed in Aim 2, we will estimate kinetic parameters for each B cell class during differentiation in the presence of sirolimus, mycophenolate mofetil, and IL-6 blocking antibodies. The stochastic branching process model developed in Aim 1 will be used to predict experimental outcomes and compare them with in vitro data. [unreadable] [unreadable] [unreadable]